To delete rounds, on the 'Performance' tab select the round you would like to delete.
Then tap the '3 dots icon' on the top-right edge and select ‘Delete Round’.
Please make sure you are deleting the correct round, if not tap cancel and repeat the process.
If you want to do a 'fresh start', you would need to delete your rounds one by one following the above steps, and your stats will be automatically recalculated based on your saved rounds. If you have no rounds played, then your stats will go back to 'zero'.
Alternatively, if you are a Premium golfer, you can simply filter your stats by date or by golf course: https://blog.hole19golf.com/new-hole19-premium-feature-stats-filtering/